Invisibility devices exploit ambiguities in the inverse scattering problem of light in media. Scattering also serves as an important general tool to infer information about the structure of matter. We elucidate the nature of scattering ambiguities that arise in central potentials. We show that scattering is a tomographic projection: The integrated scattering angle is a projection of a scattering function onto the impact parameter. This function depends on the potential but may be multivalued, allowing for ambiguities where several potentials share the same scattering data. In addition, multivalued scattering angles also lead to ambiguities. We apply our theory to show that it is, in principle, possible to construct an invisibility device without infinite phase velocity of light.

We propose a scheme to generate double electromagnetically induced transparency and optimal cross-phase modulation for two slow, copropagating pulses with matched group velocities in a single species of atom, namely ${}^{87}\mathrm{Rb}$. A single pump laser is employed and a homogeneous magnetic field is utilized to avoid cancellation effects through the nonlinear Zeeman effect. We suggest a feasible preparational procedure for the atomic initial state to achieve matched group velocities for both signal fields.

Electrosprays have diverse applications including protein analysis, electrospinning, and nanoencapsulation for drug delivery. We show that a variety of electrospray regimes exhibit fundamental analogy with the nonlinear dynamics of a dripping faucet. The applied voltage in electrosprays results in additional period doublings and temporal order-chaos-order transitions. Attractors in the return maps show logarithmic self-similarity in time, suggesting self-similar capillary waves on the meniscus. The bifurcations in ejection time can be explained by phase variations between capillary waves and pinch-off conditions and by ejection mode changes due to contact angle variations.

We investigate experimentally and theoretically the coalescence dynamics of two spreading droplets on a highly wettable substrate. Upon contact, surface tension drives a rapid motion perpendicular to the line of centers that joins the drops and lowers the total surface area. We find that the width of the growing meniscus bridge between the two droplets exhibits power-law behavior, growing at early times as $t^{1/2}$. Moreover, the growth rate is highly sensitive to both the radii and heights of the droplets at contact, scaling as $h_o^{3/2}/R_o$. This size dependence differs significantly from the behavior of freely suspended droplets, in which the coalescence growth rate depends only weakly on the droplet size. We demonstrate that the scaling behavior is consistent with a model in which the growth of the meniscus bridge is governed by the viscously hindered flux from the droplets.

The classical “brick wall,” which may, according to quantum mechanics, leak via tunneling, is here shown to be completely transparent when appropriate impedance matching media are placed both in front of and behind the “wall.” Optical experiments involving beyond-critical-angle-tunnel barriers in the frustrated total internal reflection scheme which mimic quantum mechanical systems provide convincing proof of this remarkable effect. The same mechanism also allows vastly enhanced transmission through unstructured thin metal films without the need for surface wave excitation.

A coronagraph designed for high contrast imaging applications has been experimentally tested using coherent laser light and a vortex mask of topological charge $m=2$. Intensity contrast values of 95% were achieved in this first verification of the scheme. Improvements for approaching the theoretical value of 100% are suggested.

The deformation and breakup of a drop in an immiscible equiviscous liquid undergoing unbounded shear flow has been extensively investigated in the literature, starting from the pioneering work of Taylor. In this Letter, we address the case of microconfined shear flow, a problem which is relevant for microfluidics and emulsion processing applications. The main effects of confinement include complex oscillating transients and drop stabilization against breakup. In particular, very elongated drop shapes are observed, which would be unstable in the unbounded case and can be explained in terms of wall-induced distortion of the shear flow field. We show that wall effects can be exploited to obtain nearly monodisperse emulsions in microconfined shear flow.

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green’s functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.

We report spatiotemporal pattern formation in Taylor-Couette flow (i.e., flow between rotating cylinders) of viscoelastic dilute polymer solutions obtained for the first time from first-principles dynamical simulations. Solution structures with varying spatial and temporal symmetries, such as rotating standing waves, flames, disordered oscillations, and solitary vortex solutions which include diwhirls (stationary and axisymmetric) and oscillatory strips (axisymmetric or nonaxisymmetric), are observed, depending on the ratio of fluid relaxation time to the time period of inner cylinder rotation. The flow-microstructure coupling mechanisms underlying the pattern formation process are also discussed.

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.

The magnetic field measured in the Madison dynamo experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest-growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency.

We present an experimental study of a low-Reynolds number shear flow between two surfaces, one of which has a regular grooved texture augmented with a superhydrophobic coating. The combination reduces the effective fluid-surface contact area, thereby appreciably decreasing the drag on the surface and effectively changing the macroscopic boundary condition on the surface from no slip to limited slip. We measure the force on the surface and the velocity field in the immediate vicinity on the surface (and thus the wall shear) simultaneously. The latter facilitates a direct assessment of the effective slip length associated with the drag reduction.

We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling.

We report the experimental verification of the predicted chaotic mixing characteristics for a polydimethylsioxane microfluidic chip, based on the mechanism of multistage cross-channel flows. While chaotic mixing can be achieved within short passage distances, there is an optimal side channel flow pulsation frequency beyond which the mixing becomes ineffective. Based on the physical understanding of a Poincaré section analysis, we propose the installation of passive flow baffles in the main microfluidic channel to facilitate high-frequency mixing. The combined hybrid approach enables chaotic mixing at enhanced frequency and reduced passage distance in two-dimensional flows.

We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show that wave collapse can be prevented. We corroborate these experimental results with numerical simulations of the ($2+1$)-dimensional focusing cubic nonlinear Schrödinger equation with piecewise constant coefficients and a theoretical analysis of this setting using a moment method.

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general Hamiltonian systems. We also demonstrate that the nodal domains of the perturbed cat maps obey the Cardy crossing formula and find evidence that the boundaries of the nodal domains are described by stochastic Loewner evolution with diffusion constant $\kappa$ close to the expected value of 6, suggesting that quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.

We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.

We report the first observation of the dependence of the coherent-backscattering (CBS) enhanced cone with the frequency of the backscattered photon. The experiment is performed on a diffusing liquid suspension and the Doppler broadening of light is induced by the Brownian motion of the scatterers. Heterodyne detection on a CCD camera is used to measure the complex field (i.e., the hologram) of the light that is backscattered at a given frequency. The analysis of the holograms yield the frequency and the propagation direction of the backscattered photons. We observe that the angular CBS cone becomes more narrow in the tail of the Brownian spectrum. The experimental results are in good agreement with a simple theoretical model.

The background of three-dimensional hydrodynamic (vortical) fluctuations in a stochastically forced, laminar, incompressible, plane Couette flow is simulated numerically. The fluctuating field is anisotropic and has well pronounced peculiarities: (i) the hydrodynamic fluctuations exhibit nonexponential, transient growth; (ii) fluctuations with the streamwise characteristic length scale about 2 times larger than the channel width are predominant in the fluctuating spectrum instead of streamwise constant ones; (iii) nonzero cross correlations of velocity (even streamwise-spanwise) components appear; (iv) stochastic forcing destroys the spanwise reflection symmetry (inherent to the linear and full Navier-Stokes equations in a case of the Couette flow) and causes an asymmetry of the dynamical processes.

We demonstrate that ultrasmall double-layer photonic-crystal-slab cavities exhibit a very high-$Q$ value for a wide range of the layer spacing, which enables us to realize unique optomechanical coupling. By mechanically varying the separation, we can achieve extraordinarily large wavelength conversion. In addition, the light stored in the cavity can generate a large radiation force. We show that this system exhibits extremely high energy conversion efficiency between optical and mechanical energy, leading to a novel approach for the optomechanical control of light and matter.